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Exhibit (a)(1)(D)

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

Dionex Corporation

$118.50 Net Per Share

Weston D Merger Co.

an indirect wholly owned subsidiary of

Thermo Fisher Scientific Inc.

THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF WEDNESDAY, JANUARY 19, 2011, UNLESS THE OFFER IS EXTENDED.

December 20, 2010

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

Weston D Merger Co., a Delaware corporation (“Purchaser”) and an indirect wholly owned subsidiary of Thermo Fisher Scientific Inc., a Delaware corporation (“Thermo Fisher”), is making an offer to purchase all outstanding shares of common stock, par value $0.001 per share, of Dionex Corporation (the “Shares”), a Delaware corporation (“Dionex”), at a purchase price of $118.50 per Share, net to the seller in cash, without interest, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated December 20, 2010 (the “Offer to Purchase”), and in the related Letter of Transmittal (which, together with any amendments or supplements thereto, collectively constitute the “Offer”) enclosed herewith.

Please furnish copies of the enclosed materials to those of your clients for whose accounts you hold Shares registered in your name or in the name of your nominee.

Enclosed herewith for your information and forwarding to your clients are copies of the following documents:

1. Offer to Purchase dated December 20, 2010.

2. The Letter of Transmittal for your use in accepting the Offer and tendering Shares and for the information of your clients. Facsimile copies of the Letter of Transmittal may be used to tender Shares.

3. Notice of Guaranteed Delivery to be used to accept the Offer if certificates for Shares and all other required documents cannot be delivered to American Stock Transfer & Trust Company (the “Depositary”), or if the procedures for book-entry transfer cannot be completed, by the expiration date of the Offer.

4. A letter that may be sent to your clients for whose accounts you hold Shares registered in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Offer.

5. Dionex’s Solicitation/Recommendation Statement on Schedule 14D-9.

6. Internal Revenue Service Form W-9.

7. Return envelope addressed to the Depositary.

YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT

12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF WEDNESDAY, JANUARY 19, 2011, UNLESS THE OFFER IS EXTENDED.

The Offer is being made pursuant to an Agreement and Plan of Merger dated as of December 12, 2010 (the “Merger Agreement”), among Thermo Fisher, Purchaser and Dionex. The Merger Agreement provides, among other things, that after consummation of the Offer, Purchaser will merge with and into Dionex (the “Merger”), with Dionex continuing as the surviving corporation and an indirect wholly owned subsidiary of Thermo Fisher. At the effective time of the Merger, each outstanding Share (other than any Shares held by Thermo Fisher, Purchaser, Dionex or any direct or indirect wholly owned subsidiary of Dionex, and any shares held by stockholders who validly exercise their appraisal rights in connection with the Merger ) will be cancelled and extinguished and automatically converted into the right to receive the price per Share paid in the Offer, without interest.

The Board of Directors of Dionex (the “Dionex Board”) has unanimously (i) determined that the Merger Agreement and the transactions contemplated by the Merger Agreement, including the Offer and the Merger, are advisable and in the best interests of Dionex stockholders and (ii) adopted the Merger Agreement and approved the transactions contemplated by the Merger Agreement, including the Offer and the Merger, in accordance with the requirements of the General Corporation Law of the State of Delaware. The Dionex Board recommends that Dionex stockholders accept the Offer and tender their Shares in the Offer and (if required by Delaware law) adopt the Merger Agreement.

The Offer is conditioned upon, among other things, (i) there being validly tendered in accordance with the terms of the Offer, prior to the expiration date of the Offer and not withdrawn, a number of Shares that, together with the Shares then owned by Thermo Fisher and/or Purchaser, represents at least a majority of the total number of Shares outstanding on a fully diluted basis and (ii) expiration or termination of the applicable waiting period (and any extension thereof) under the Hart-Scott-Rodino Antitrust Improvement Act of 1976, as amended, and the regulations promulgated thereunder, and there having been obtained required or advisable foreign antitrust clearances. The Offer is also subject to the other conditions described in the Offer to Purchase.

Upon the terms and subject to the conditions of the Offer (including, if the Offer is extended or amended, the terms and conditions of any such extension or amendment), Purchaser will be deemed to have accepted for payment, and will pay for, all Shares validly tendered and not properly withdrawn by the expiration date of the Offer if and when Purchaser gives oral or written notice to the Depositary of Purchaser’s acceptance of the tenders of such Shares for payment pursuant to the Offer. In all cases, Purchaser will pay for Shares accepted for payment pursuant to the Offer only after timely receipt by the Depositary of (a) certificates representing such Shares or timely confirmation of a book-entry transfer of such Shares into the Depositary’s account at the Book-Entry Transfer Facility (as defined in the Offer to Purchase) (“Book-Entry Confirmation”) pursuant to the procedures set forth in Section 3 of the Offer to Purchase; (b) a properly completed and duly executed Letter of Transmittal (or facsimile thereof) with all required signature guarantees or, in the case of a book-entry transfer, an Agent’s Message (as defined in Section 3 of the Offer to Purchase) in lieu of the Letter of Transmittal; and (c) any other documents required by the Letter of Transmittal. Accordingly, tendering stockholders may be paid at different times depending upon when certificates for Shares or Book-Entry Confirmations with respect to Shares are actually received by the Depositary. Under no circumstances will interest be paid on the consideration paid for Shares pursuant to the Offer, regardless of any extension of the Offer or any delay in making payment for Shares.

Purchaser is not aware of any jurisdiction where the making of the Offer is prohibited by any administrative or judicial action pursuant to any valid state statute. If Purchaser becomes aware of any valid state statute prohibiting the making of the Offer or the acceptance of the Shares, Purchaser will make a good faith effort to comply with that state statute. If, after a good faith effort, Purchaser cannot comply with the state statute, Purchaser will not make the Offer to, nor will Purchaser accept tenders from or on behalf of, the holders of Shares in that state. In any jurisdiction where the securities, blue sky or other laws require the Offer to be made by a licensed broker or dealer, the Offer will be deemed to be made on behalf of Purchaser or by one or more registered brokers or dealers licensed under the laws of such jurisdiction.

Purchaser will not pay any fees or commissions to any broker, dealer or other person (other than Innisfree M&A Incorporated (the “Information Agent”), the dealer managers for the Offer and the Depositary as described in the Offer to Purchase) for soliciting tenders of Shares pursuant to the Offer. Purchaser will, however, upon request, reimburse brokers, dealers, commercial banks and trust companies for customary mailing and handling costs incurred by them in forwarding the enclosed materials to their customers.

Purchaser will pay all stock transfer taxes applicable to its purchase of Shares pursuant to the Offer, subject to Instruction 6 of the Letter of Transmittal.

If holders of Shares wish to tender, but it is impracticable for them to forward their certificates or other required documents or to complete the procedures for delivery by book-entry transfer prior to the expiration of the Offer, a tender may be effected by following the guaranteed delivery procedures described in Section 3 of the Offer to Purchase.

Any inquiries you may have with respect to the Offer should be addressed to, and additional copies of the enclosed materials may be obtained from, the Information Agent at its address and telephone numbers set forth on the back cover of the Offer to Purchase.

Very truly yours,

Thermo Fisher Scientific Inc.

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU THE AGENT OF THERMO FISHER, PURCHASER, DIONEX, THE INFORMATION AGENT, THE DEALER MANAGERS FOR THE OFFER OR THE DEPOSITARY, OR ANY AFFILIATE OF ANY OF THEM OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE DOCUMENTS ENCLOSED HEREWITH AND THE STATEMENTS CONTAINED THEREIN.