{"id":9288,"date":"2025-10-18T02:23:49","date_gmt":"2025-10-17T18:23:49","guid":{"rendered":"https:\/\/www.andrewsun.net\/panta_rhei\/?p=9288"},"modified":"2025-10-18T02:24:18","modified_gmt":"2025-10-17T18:24:18","slug":"regular-ordinary","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9288","title":{"rendered":"regular\/ordinary"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"9288\">\n\n<p>\u5728\u6211\u7684\u9886\u57df\uff0c\u6709\u4e00\u4e2a\u6211\u4ece\u521d\u5b66\u5230\u73b0\u5728\u4e00\u76f4\u5341\u5206\u4e0d\u9002\u7684\u4e00\u4e2a\u8bcd\uff1aregular solution\u3002<\/p>\n\n\n\n<p>regular\u82f1\u8bed\u5e94\u8be5\u662f\u6309\u4e8b\u7269\u4ee5\u5f80\u7684\u5468\u671f\u53d1\u751f\u7684\u610f\u601d\uff0c\u4f46\u7f8e\u56fd\u4eba\u628a\u5b83\u7528\u4f5cordinary\uff08\u5e73\u51e1\uff09\u4e4b\u4e49\u3002\u6240\u8c13\u5e73\u51e1\u662f\u8981\u8ddf\u201c\u7279\u6b8a\u201d\u3001\u201c\u795e\u5723\u201d\u3001\u201c\u9ad8\u8d35\u201d\u3001\u201c\u7406\u60f3\u201d\u4e4b\u7c7b\u7684\u8bcd\u76f8\u5bf9\u7acb\u3002\u4e0d\u4fe1\u7684\u53ef\u4ee5\u67e5\u4e00\u4e0b\u725b\u6d25\u8bcd\u5178\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Me: I \u2018d like a cup of milk please.<br \/>Server: We have chocolate, strawberry, vanilla. Which would you like sir?<br \/>Me: I&#8217;d like a cup of ordinary milk please.<br \/>Server: We don&#8217;t have that flavor, we only have chocolate etc.<br \/>Me: No, I&#8217;d like a cup of the white stuff that comes out of a cow:<br \/>Server: Oh, you mean regular milk?<br \/>Me: Yes please, but I don&#8217;t care how often the milk comes out of the cow.<\/p>\n<\/blockquote>\n\n\n\n<p>J. Hildebrand\u2014\u2014regular solution\u4e00\u8bcd\u7684\u675c\u64b0\u8005\u2014\u2014\u5c31\u662f\u4e2a\u8001\u7f8e\u3002\u4ed6\u51fa\u751f\u3001\u6c42\u5b66\u548c\u4efb\u804c\u90fd\u5728\u7f8e\u56fd\u3002\u4ed6\u81ea\u5df1\u89e3\u91ca\u8fc7regular solution\u8fd9\u4e2a\u8bcd\u7684\u610f\u601d\u3002\u8fd9\u662f\u53e6\u4e00\u4e2a\u62ffregular\u5f53ordinary\u7528\u7684\u7f8e\u5f0f\u82f1\u8bed\u5178\u578b\u4f8b\u5b50\u3002<\/p>\n\n\n\n<p>\u7406\u60f3\u6eb6\u6db2\uff08ideal solution\uff09\u6ca1\u6709\u6df7\u5408\u70ed\uff08\u7113\uff09\uff0c\u4f46\u54ea\u6015\u662f\u53ea\u6709\u8272\u6563\u529b\u90fd\u80fd\u5fc5\u80fd\u5236\u9020\u51fa\u6df7\u5408\u70ed\u6765\u2014\u2014\u54ea\u6709\u4e24\u79cd\u5206\u5b50\u6781\u5316\u7387\u4e00\u6a21\u4e00\u6837\u7684\uff1f\u5927\u5c0f\u4e00\u6837\u7684\u5012\u662f\u53ef\u4ee5\u3002\u56e0\u6b64\u5728\u51e1\u95f4\u7684\u6eb6\u6db2\u90fd\u4e0d\u4f1a\u50cf\u7406\u60f3\u6eb6\u6db2\u90a3\u6837\u7684\u3002<\/p>\n\n\n\n<p>\u5728Hildebrand\u90a3\u4f1a\u513f\u8fd8\u6ca1\u6709\u4ec0\u4e48\u8d85\u989d\u71b5\u6548\u5e94\u7684\u62a5\u9053\u3002\u4ed6\u60f3\u7684\u5c31\u662f\u6df7\u5408\u70ed\u3002\u73b0\u5728\u6211\u4eec\u5565\u90fd\u89c1\u8fc7\u4e86\uff0c\u624d\u628a\u6b63\u89c4\u6eb6\u6db2\u5b9a\u4e49\u4e3a\u8d85\u989d\u6df7\u5408\u71b5\u4e3a\u96f6\uff1b\u6df7\u5408\u7113\u4e3a\u96f6\u5b9a\u4e49\u4e3a\u65e0\u70ed\u6eb6\u6db2\u3002<\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 9288 -->","protected":false},"excerpt":{"rendered":"<p>\u5728\u6211\u7684\u9886\u57df\uff0c\u6709\u4e00\u4e2a\u6211\u4ece\u521d\u5b66\u5230\u73b0\u5728\u4e00\u76f4\u5341\u5206\u4e0d\u9002\u7684\u4e00\u4e2a\u8bcd\uff1aregular solution\u3002 regular\u82f1\u8bed\u5e94\u8be5\u662f\u6309\u4e8b\u7269\u4ee5\u5f80\u7684\u5468\u671f\u53d1\u751f\u7684\u610f\u601d\uff0c\u4f46\u7f8e\u56fd\u4eba\u628a\u5b83\u7528\u4f5cordinary\uff08\u5e73\u51e1\uff09\u4e4b\u4e49\u3002\u6240\u8c13\u5e73\u51e1\u662f\u8981\u8ddf\u201c\u7279\u6b8a\u201d\u3001\u201c\u795e\u5723\u201d\u3001\u201c\u9ad8\u8d35\u201d\u3001\u201c\u7406\u60f3\u201d\u4e4b\u7c7b\u7684\u8bcd\u76f8\u5bf9\u7acb\u3002\u4e0d\u4fe1\u7684\u53ef\u4ee5\u67e5\u4e00\u4e0b\u725b\u6d25\u8bcd\u5178\u3002 Me: I \u2018d like a cup of milk please.Server: We have chocolate, strawberry, vanilla. Which would you like sir?Me: I&#8217;d like a cup of ordinary milk please.Server: We don&#8217;t have that flavor, we only have chocolate etc.Me: No, I&#8217;d like a cup of the white stuff that comes out of a cow:Server: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"aside","meta":{"inline_featured_image":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"J. Hildebrand\u2014\u2014regular solution\u4e00\u8bcd\u7684\u675c\u64b0\u8005\u2014\u2014\u5c31\u662f\u4e2a\u8001\u7f8e\u3002\u4ed6\u51fa\u751f\u3001\u6c42\u5b66\u548c\u4efb\u804c\u90fd\u5728\u7f8e\u56fd\u3002\u4ed6\u81ea\u5df1\u89e3\u91ca\u8fc7regular solution\u8fd9\u4e2a\u8bcd\u7684\u610f\u601d\u3002\u8fd9\u662f\u53e6\u4e00\u4e2a\u628aordinary\u5f53regular\u7528\u7684\u7f8e\u5f0f\u82f1\u8bed\u5178\u578b\u4f8b\u5b50\u3002","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[212],"tags":[150],"class_list":["post-9288","post","type-post","status-publish","format-aside","hentry","category-tagged","tag-polymer-physics","post_format-post-format-aside"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1aPvF-2pO","jetpack-related-posts":[{"id":3211,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/3211","url_meta":{"origin":9288,"position":0},"title":"Taylor\u4e0e\u6db2\u6ef4\u53d8\u5f62","author":"Andrew","date":"2011\u5e747\u670811\u65e5","format":false,"excerpt":"\u6211\u7684\u5e08\u5f1f\u8981\u505a\u4e73\u6db2\u4f53\u7cfb\u3002\u6211\u4e00\u5f00\u59cb\u7684idea\u662f\u57fa\u4e8e\u9ad8\u4f53\u7cfb\u5206\u6570\u7684\u4e73\u6db2\uff0c\u4f46\u6162\u6162\u53d1\u73b0\u505a\u6db2\u6ef4\u53d8\u5f62\u53cd\u800c\u66f4\u597d\u5730\u4f53\u7cfb\u6211\u7684idea\u3002\u4e00\u5f00\u59cb\u60f3\u7740\u662f\u5e08\u5f1f\u7684\u8bfe\u9898\uff0c\u8981\u8003\u8651\u5728\u4ed6\u7684\u6c34\u5e73\u529b\u6240\u80fd\u53ca\u7684\u8303\u56f4\u5185\u505a\uff0c\u4e8e\u662f\u6211\u4e00\u76f4\u90fd\u53ea\u544a\u8bc9\u4ed6\u8981\u5e72\u54ea\u51e0\u4ef6\u5927\u4e8b\uff0c\u770b\u54ea\u51e0\u65b9\u9762\u7684\u5185\u5bb9\uff0c\u89e3\u51b3\u54ea\u4e9b\u95ee\u9898\u3002\u4f46\u6211\u81ea\u5df1\u6ca1\u6709\u8ddf\u7740\u53bb\u770b\u6db2\u6ef4\u53d8\u5f62\u7684\u6587\u732e\u3002\u6700\u8fd1\u53d1\u73b0\u8fd9\u6837\u597d\u50cf\u5bb9\u6613\u53d1\u751f\u8bef\u89e3\u548c\u8d70\u504f\u3002\u4e3b\u8981\u56e0\u4e3a\u8fd9\u662f\u6211\u7684\u800c\u4e0d\u662f\u4ed6\u7684idea\uff0c\u6211\u7684\u6700\u7ec8\u610f\u56fe\u4e0d\u662f\u8bf4\u4e00\u4e24\u6b21\u5c31\u80fd\u8bb2\u660e\u767d\u4ed6\u3002\u6240\u4ee5\u73b0\u5728\u89c9\u5f97\u8fd8\u662f\u6211\u548c\u4ed6\u4e00\u540c\u5b66\u4e60\u6bd4\u8f83\u597d\u3002\u4f46\u6211\u4ecd\u7136\u8981\u6ce8\u610f\u8be5\u4ed6\u61c2\u7684\u4e1c\u897f\u5c31\u7b97\u6211\u770b\u61c2\u4e86\u8fd8\u662f\u5f97\u4ed6\u770b\u4e00\u904d\uff0c\u518d\u600e\u4e48\u201c\u4e00\u540c\u5b66\u4e60\u201d\uff0c\u5c06\u6765\u662f\u4ed6\u7b54\u8fa8\u4e0d\u662f\u6211\u7b54\u8fa9\u2014\u2014\u8fd9\u662f\u6700\u57fa\u672c\u7684\u5e95\u7ebf\u3002 \u6240\u4ee5\u4eca\u5929\u4e0a\u5348\u7565\u5fae\u67e5\u4e86\u4e00\u4e0b\u6587\u732e\u3002\u6211\u5c31\u53d1\u73b0\u65b0\u624b\u548c\u8001\u624b\u7684\u533a\u522b\u786e\u5b9e\u5f88\u660e\u663e\u3002\u6211\u8ba9\u5e08\u5f1f\u770b\u5173\u4e8e\u4e73\u6db2\u7684\u6587\u732e\uff0c\u8fd9\u4e48\u4e45\u4e86\uff0c\u4ed6\u597d\u50cf\u5e76\u6ca1\u6709\u6478\u6e05\u7814\u7a76\u7684\u4e3b\u7ebf\u3002\u7ed3\u679c\u6211\u4e00\u4e0a\u5348\u5c31\u641e\u597d\u4e86\u3002\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bb2\uff0c\u6211\u624d\u53d1\u73b0\u6211N\u4e45\u4ee5\u524d\u5728\u79d1\u5b66\u7f51\u4e0a\u5199\u7684\u90a3\u4e2a\u201c\u6211\u9605\u8bfb\u6587\u732e\u7684\u505a\u6cd5\u201d\u786e\u5b9e\u6bd4\u8f83\u6709\u5b9e\u9645\u610f\u4e49\u3002\u73b0\u5728\u8fd9\u7bc7\u4e1c\u897f\u597d\u50cf\u88ab\u8f6c\u6765\u8f6c\u53bb\uff0c\u4f46\u662f\u539f\u51fa\u5904\u968f\u7740\u6211\u5220\u6389\u79d1\u5b66\u7f51\u5e10\u6237\u4e5f\u4e00\u8d77\u6d88\u5931\u4e86\u3002\u73b0\u5728\u6211\u5728\u672c\u535a\u5ba2\u91cd\u65b0\u8d34\u4e86\u51fa\u6765\uff0c\u91cc\u9762\u4f5c\u4e86\u4e00\u4e9b\u5c0f\u4fee\u6539\uff0c\u57fa\u672c\u4e0a\u6309\u5f53\u65f6\u5199\u7684\u539f\u6837\u4fdd\u7559\uff0c\u4ee5\u4f9b\u65e5\u540e\u53c2\u8003\u3002 \u4eca\u5929\u4e0a\u5348\u770b\u5230\u4e86\u5173\u4e8e\u6d6e\u6db2\u4e2d\u7684\u6db2\u6ef4\u53d8\u5f62\u4e0e\u7c98\u5f39\u6027\u5173\u7cfb\u7684\u7406\u8bba\u7814\u7a76\u3002\u4eceEinstein\u3001Taylor\u3001Palierne\u518d\u5230\u540e\u9762\u7684M&M\u3002Einstein\u7684\u7406\u8bba\u90a3\u4e2a\u201c2.5\u03c6\u201d\u7684\u6a21\u578b\u5f53\u7136\u662f\u53ea\u9002\u5408\u5355\u5206\u6563\u786c\u7403\u4f53\u7cfb\u3002\u9996\u5148\u8003\u8651\u6db2\u6ef4\u4f53\u7cfb\u7684\u662fTaylor\u3002\u4f46\u6211\u8fd8\u662f\u770b\u4e0d\u61c2Taylor\u539f\u6587\u91cc\u7684\u63a8\u5bfc\u662f\u600e\u4e48\u201c\u4ece\u786c\u5230\u8f6f\u201d\u7684\u3002\u8fd9\u6ca1\u6240\u8c13\uff0c\u53ef\u4ee5\u901a\u8fc7\u770b\u540e\u4eba\u5bf9Taylor\u65b9\u6cd5\u7684\u590d\u8ff0\u6765\u770b\u61c2\u3002 \u6309\u7167\u6700\u5e38\u89c1\u7684\u5f15\u7528Taylor\u7684\u539f\u6587\u662f\u4e24\u7bc7\u53d1\u8868\u5728Proc. R. Soc. A\u4e0a\u7684\u6587\u7ae0\u3002\u5927\u81f4\u4e0a\u8bb2\u7b2c\u4e00\u7bc7\u662f\u7406\u8bba\uff0c\u7b2c\u4e8c\u7bc7\u662f\u5b9e\u9a8c\u3002\u8ba9\u6211\u5927\u611f\u5174\u8da3\u7684\u7b2c\u4e8c\u7bc7\u6587\u7ae0\u91cc\u7684\u5404\u79cdapparatuses\u2020\uff1a \u6709\u4e24\u4e2a\u4e3b\u8981\u5b9e\u9a8c\u4eea\u5668\uff0c\u662f\u4e3a\u6db2\u6ef4\u53d8\u5f62\u5236\u9020\u6d41\u573a\u73af\u5883\u7684\u3002\u4e00\u4e2a\u662f\u201cfour roller apparatus\u201d\uff0c\u5236\u9020\u53cc\u66f2\u7ebf\u6d41\uff1b\u4e00\u4e2a\u662f\u201cparallel band apparatus\u201d\uff0c\u5236\u9020\u7b80\u5355\u526a\u5207\u3002 \u00a0 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key TO xxx\uff0c\u6240\u4ee5\u660e\u660e\u672c\u571f\u82f1\u8bed\u662f\u8bf4the key for the office\u7684\uff0c\u7ed9\u4e2d\u56fd\u4eba\u8bf4\u591a\u4e86\u5c31\u53d8\u6210the key to the office\u4e86\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"Four roller 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1993)\u200b\u200b*\u200b\uff0c\u6211\u5199\u7684\u5185\u5bb9\u5927\u90e8\u5206\u90fd\u662f\u76f4\u63a5\u6765\u81ea\u8fd9\u91cc\u3002\u5176\u5b9e\u6211\u4e5f\u72ec\u7acb\u5730\u8bc4\u4f30\u8fc7\u5979\u7684\u8bba\u6587\u3002\u6211\u81ea\u5df1\u770b\u8fc7\u4e00\u90e8\u5206\u7684\u5386\u53f2\u6587\u732e\u7684\u539f\u6587\uff08\u89c1\u6b64\u6587\uff09\uff0c\u518d\u53bb\u770bIanniello\u5bf9\u8fd9\u4e9b\u539f\u6587\u7684\u89e3\u8bfb\uff0c\u89c9\u5f97\u5979\u5173\u6ce8\u7ec6\u8282\u8ddf\u6211\u4e00\u6837\u591a\uff0c\u751a\u81f3\u770b\u5f97\u548c\u60f3\u5f97\u6bd4\u6211\u66f4\u4ed4\u7ec6\u3002\u79d1\u5b66\u54f2\u5b66\u5c42\u9762\u4e0a\u7684\u5173\u7167\u89d2\u5ea6\u4e5f\u548c\u6211\u5f88\u63a5\u8fd1\uff0c\u56e0\u6b64\u6211\u5f88\u4fe1\u8d56\u8fd9\u4e2a\u5de5\u4f5c\u3002\u53e6\u5916\u8fd8\u6709\u4e00\u7bc7\u66f4\u65e9\u4e9b\u7684\u79d1\u5b66\u53f2\u8bba\u6587\u200b(D\u00f6rries 1991)\u200b\uff0c\u4ece\u5e7f\u4e49\u7684\u201c\u4f59\u6548\u201d\uff08Nachwirking\uff09\u4e0e\u201c\u8fdf\u6ede\u201d\uff08histeresis\uff09\u6982\u5ff5\u7684\u89d2\u5ea6\u56de\u987e\u4e8619\u4e16\u7eaa\u7684\u7269\u7406\u5b66\u53f2\uff0c\u4f46\u662f\u63cf\u8ff0\u4e0d\u5982Ianniello\u7684\u6587\u7ae0\u8be6\u7ec6\u3002\u9664\u4e86\u8fd9\u4e9b\u79d1\u5b66\u53f2\u7814\u7a76\u8005\u7684\u8bba\u6587\u5916\uff0c\u6211\u5728\u8fd9\u91cc\u63d0\u4e00\u4e9b\u6d41\u53d8\u5b66\u5bb6\u81ea\u5df1\u505a\u7684\u5386\u53f2\u603b\u7ed3\u3002\u200b(Tanner and Walters 1998)\u200b\u7684\u8fd9\u672c\u4e66\u662f\u6574\u4e2a\u6d41\u53d8\u5b66\u7684\u4e00\u4e2a\u5927\u7684\u5386\u53f2\u603b\u7ed3\uff0c\u662f\u4e00\u4e2a\u5f88\u4f1f\u5927\u7684\u5de5\u7a0b\uff0c\u4f46\u662f\u96be\u514d\u4e5f\u6d41\u4e8e\u6cdb\u6cdb\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u7c97\u7565\u7684\u63d0\u7eb2\u548c\u53c2\u8003\u6587\u732e\u6765\u53c2\u8003\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0cHershel Markovitz\u505a\u8fc7\u7684\u5f88\u591a\u6d41\u53d8\u5b66\u53f2\u603b\u7ed3\u66f4\u52a0\u95ee\u9898\u5bfc\u5411\u56e0\u800c\u4e5f\u66f4\u5bcc\u6709\u6d1e\u89c1\u200b(Markovitz 1968, 1977, 1985)\u200b\u3002\u200b(Doraiswamy 2002)\u200b\u4e5f\u505a\u4e86\u4e00\u4e2a\u5f88\u5168\u9762\u7684\u5386\u53f2\u6eaf\u6e90\u8d44\u6599\u603b\u7ed3\u3002\u200b(Tanner 2002)\u200b\u603b\u7ed3\u4e86\u6d41\u53d8\u6d4b\u91cf\u5b66\u4e2d\u6b63\u5f26\u6d4b\u8bd5\u65b9\u6cd5\u7684\u5386\u53f2\u3002 \u5df2\u6545\u7684\u6d41\u53d8\u5b66\u5bb6\u90d1\u878d\u8001\u5e08\u5728\u79d1\u5b66\u7f51\u4e0a\u7684\u535a\u5ba2\u5199\u6ee1\u4e86\u810d\u7099\u4eba\u53e3\u7684\u6d41\u53d8\u5b66\u53f2\u8bdd\u3002 1. \u4eca\u5929\u77e5\u9053\u7684\u201c\u7c98\u5f39\u6027\u201d \u201c\u7c98\u5f39\u6027\u201d\uff08viscoelasticity\uff09\u662f\u6d41\u53d8\u5b66\u6216\u529b\u5b66\u65b9\u9762\u7684\u8bcd\u3002 Ferry\u5bf9\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u5b8f\u89c2\u552f\u8c61\u7406\u8bba\u6a21\u578b\u548c\u5b9e\u9a8c\u65b9\u6cd5\u8fdb\u884c\u4e86\u5b8c\u6574\u7684\u603b\u7ed3\u200b(Ferry 1980)\u200b\u3002\u800c\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u5c31\u662f\u6574\u4e2a\u6d41\u53d8\u5b66\u7684\u7814\u7a76\u5bf9\u8c61\uff0c\u5176\u73b0\u8c61\u5b66\u6a21\u578b\u548c\u5b9e\u9a8c\u65b9\u6cd5\u53ef\u89c1\u4e8e\u5404\u4e2a\u6d41\u53d8\u5b66\u6559\u6750\u3002\u503c\u63d0\u4e00\u63d0\u7684\u662f\u632f\u8361\u6d4b\u8bd5\u5728\u975e\u7ebf\u6027\u54cd\u5e94\u4e2d\u7684\u63cf\u8ff0\u6846\u67b6\u5728\u6d41\u53d8\u5b66\u4e2d\u7684\u5e94\u7528\u662f\u201c\u5927\u5e45\u632f\u8361\u526a\u5207\u201d\uff08large amplitude oscillatory shear\uff0cLAOS\uff09\u3002\u8fd9\u65b9\u9762\u6700\u8fd1\u7684\u5927\u578b\u7efc\u8ff0\u200b(Hyun et al. 2011)\u200b\u5df2\u7ecf\u5f88\u65e9\u4e86\uff0c\u5176\u4e4b\u540e\u503c\u5f97\u5173\u6ce8\u7684\u76f8\u5173\u7efc\u8ff0\u6709\u200b(Bird and Giacomin 2016)\u200b\u548c\u200b(Voigtmann 2014)\u200b\u3002 \u4e8b\u5b9e\u4e0a\u7c98\u5f39\u6027\u7684\u73b0\u8c61\u5728\u529b\u5b66\u4e4b\u5916\u6709\u66f4\u4e00\u822c\u7684\u672c\u8d28\uff0c\u5b83\u5b9e\u8d28\u4e0a\u662f\u4e00\u79cd\u677e\u5f1b\uff08\u5f1b\u8c6b\uff09\u73b0\u8c61\u200b\u2020\u200b\uff0c\u5728\u7535\u78c1\u5b66\u4e2d\u4e5f\u5f88\u666e\u904d\u3002\u56e0\u6b64Oppenheim\u7684\u7ecf\u5178\u6559\u79d1\u4e66\u200b(Oppenheim et al. 1997)\u200b\u4e2d\u7684\u5f88\u591a\u65b9\u6cd5\u8ddf\u7c98\u5f39\u6027\u73b0\u8c61\u5b66\u662f\u76f8\u901a\u7684\u3002\u4f8b\u5982\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u901a\u7528\u672c\u6784\u2014\u2014Boltzmann\u65b9\u7a0b\u5c31\u662f\u4e00\u4e2a\u7ebf\u6027\u65f6\u4e0d\u53d8\u7cfb\u7edf\u7684\u5377\u79ef\u5f0f\u3002\u5728\u540e\u9762\u7684\u5386\u53f2\u4ecb\u7ecd\u4e2d\u6211\u4eec\u5c06\u4f1a\u770b\u5230\uff0c\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u53f2\u8ddf\u7535\u78c1\u5b66\u548c\u7535\u4fe1\u6280\u672f\u7684\u53d1\u5c55\u662f\u5bc6\u5207\u76f8\u5173\u7684\u3002\u4e00\u9886\u57df\u7684\u6982\u5ff5\u6216\u65b9\u6cd5\u5ef6\u7528\u4e8e\u53e6\u4e00\u9886\u57df\u7684\u60c5\u51b5\u5f88\u5e38\u89c1\uff0c\u4e14\u8fd9\u79cd\u60c5\u51b5\u4e00\u76f4\u5ef6\u7eed\u5230\u4eca\u5929\u3002 \u81f3\u4e8e\u5b8f\u89c2\u7c98\u5f39\u6027\u6216\u5176\u4ed6\u5b8f\u89c2\u6027\u8d28\u7684\u5f1b\u8c6b\u73b0\u8c61\u7684\u5fae\u89c2\u672c\u8d28\uff0c\u5219\u662f\u975e\u5e73\u8861\u6001\u7edf\u8ba1\u529b\u5b66\u63d0\u4f9b\u7684\u3002\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u8bf4\u5b8f\u89c2\u6027\u8d28\u7684\u5f1b\u8c6b\u73b0\u8c61\u7684\u5fae\u89c2\u672c\u8d28\u5c31\u662f\u70ed\u8fd0\u52a8\u3002\u5177\u4f53\u5730\uff0c\u7ebf\u6027\u54cd\u5e94\u7406\u8bba\u662f\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7edf\u8ba1\u57fa\u7840\u3002\u8fd9\u65b9\u9762\u5185\u5bb9\u53ef\u4ee5\u53c2\u8003\u200b(Evans and Morriss 2008)\u200b\u548c\u200b(Kreuzer 1981)\u200b\u3002 \u4e0a\u8ff0\u5f15\u7528\u7684\u8d44\u6599\u4ee3\u8868\u4e86\u6211\u4eec\u4eca\u5929\u5bf9\u7c98\u5f39\u6027\u7684\u8ba4\u8bc6\u3002\u5728\u56de\u987e\u7c98\u5f39\u6027\u7684\u7814\u7a76\u5386\u53f2\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5c31\u81ea\u7136\u4f1a\u5173\u6ce8\u5f53\u65f6\u7684\u4eba\u4ece\u5f53\u65f6\u7684\u6570\u5b66\u548c\u7269\u7406\u5b66\u57fa\u7840\u548c\u5b9e\u9a8c\u73b0\u8c61\u6240\u80fd\u5f62\u6210\u7684\u6700\u521d\u8ba4\u8bc6\u8ddf\u4eca\u5929\u8ba4\u8bc6\u7684\u5dee\u5f02\u548c\u5dee\u8ddd\u662f\u600e\u6837\u7684\uff1f\u4e4b\u540e\u662f\u5982\u4f55\u201c\u677e\u5f1b\u201d\u5230\u4eca\u5929\u7684\u8ba4\u8bc6\u7684\uff1f 2. \u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u4e0e\u70ed\u529b\u5b66 \u6211\u4eec\u4eca\u5929\u7684\u8ba4\u8bc6\u4f53\u7cfb\u4e2d\uff0c\u7c98\u5f39\u6027\u73b0\u8c61\u662f\u5bf9\u7ecf\u5178\u7684\u864e\u514b\u5f39\u6027\u548c\u725b\u987f\u7c98\u6027\u7684\u63a8\u5e7f\u3002\u4ece\u66f4\u5927\u7684\u89d2\u5ea6\u770b\uff0c\u7c98\u5f39\u6027\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u4e2d\u7684\u7279\u6b8a\u672c\u6784\u5173\u7cfb\u3002\u4eca\u5929\u5982\u679c\u6211\u4eec\u8981\u8bb2\u8ff0\u7c98\u5f39\u6027\uff0c\u6211\u4eec\u4f1a\u5e0c\u671b\u542c\u4f17\u5df2\u7ecf\u5bf9\u4e0a\u8ff0\u8fd9\u4e9b\u80cc\u666f\u6709\u6240\u4e86\u89e3\u200b\u2021\u200b\u3002 \u9996\u5148\u662f\u8fde\u7eed\u4ecb\u8d28\u529b\u5b66\u3002\u6b27\u62c9\u628a\u725b\u987f\u8fd0\u52a8\u5b9a\u5f8b\u63a8\u5e7f\u81f3\u8fde\u7eed\u4ecb\u8d28\uff0c\u5e76\u63a8\u5bfc\u4e86\u521a\u4f53\u548c\u7406\u60f3\u6d41\u4f53\u7684\u65b9\u7a0b\u200b(Truesdell 1960a, 1968)\u200b\u200b\u00a7\u200b\u3002\u8fd9\u5927\u6982\u662f\u5341\u516b\u4e16\u7eaa\u4e2d\u53f6\u7684\u4e8b\u60c5\u3002 \u5173\u4e8e\u80fd\u91cf\u5b88\u6052\uff0c\u4e5f\u8bb8\u4f2f\u52aa\u5229\u7684\u5de5\u4f5c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u79cd\u4ee3\u8868\uff0c\u4ee5\u4ed61738\u5e74\u53d1\u8868\u7684Hydrodynamica\u4e3a\u6807\u5fd7\u200b(Truesdell 1960a, 1968)\u200b\u3002\u4f2f\u52aa\u5229\u65b9\u7a0b\uff0c\u5c31\u662f\u673a\u68b0\u80fd\u4e0e\u91cd\u529b\u52bf\u80fd\u4e4b\u95f4\u7684\u80fd\u91cf\u5b88\u6052\u3002\u4ec5\u8003\u8651\u8fd9\u4e24\u79cd\u80fd\u91cf\u4e4b\u95f4\u7684\u5b88\u6052\u662f\u7ecf\u5178\u529b\u5b66\u53d1\u5c55\u8fc7\u7a0b\u4e2d\u7684\u4e00\u4e2a\u4e3b\u8981\u7684\u95ee\u9898\u5f62\u5f0f\u3002\u70ed\u529b\u5b66\u610f\u4e49\u4e0a\u7684\u80fd\u91cf\u5b88\u6052\uff08\u5373\u4f5c\u4e3a\u516c\u8bbe\u7684\u70ed\u529b\u5b66\u7b2c\u4e00\u5b9a\u5f8b\uff09\uff0c\u5219\u4e0e\u70ed\u7684\u672c\u8d28\u95ee\u9898\u548c\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u8ba4\u8bc6\u7b49\u4e00\u540c\u7ea0\u7f20\u523019\u4e16\u7eaa\u4e2d\u671f\u624d\u7b97\u786e\u7acb\u3002\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":8116,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/8116","url_meta":{"origin":9288,"position":2},"title":"C. Truesdell\u6587\u7ae0\u9009\u6bb5\u8d4f\u8bfb\uff08\u4e8c\uff09","author":"Andrew","date":"2021\u5e741\u670815\u65e5","format":false,"excerpt":"Of course these discoveries have brought with them different attitudes toward theories of nature. Those who push forward the frontiers of experiment cannot wait for the thoughtful, critical, and hence cautious and slow analysis that mathematics has always demanded. Mathematicians, for their part, cannot afford to waste their time on\u2026","rel":"","context":"In &quot;\u6211\u7684\u7814\u7a76\u7b14\u8bb0&quot;","block_context":{"text":"\u6211\u7684\u7814\u7a76\u7b14\u8bb0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/rheo"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2925,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/2925","url_meta":{"origin":9288,"position":3},"title":"\u7f8e\u4e3d\u7684Calligraphy","author":"Andrew","date":"2011\u5e745\u67081\u65e5","format":false,"excerpt":"\u6211\u53d1\u73b0\u6211\u4e4b\u6240\u4ee5\u5728\u665a\u5e74\u5bf9\u5f88\u591a\u77e5\u8bc6\u65e9\u6709\u5370\u8c61\uff0c\u662f\u56e0\u4e3a\u6211\u5728\u65e9\u5e74\u65e0\u610f\u63a5\u89e6\u5230\u4e4b\u540e\u5c31\u4e00\u76f4\u8bb0\u7740\u3002\u867d\u7136\u6211\u4e00\u76f4\u8bb0\u7740\u7684\u4e1c\u897f\u662f\u975e\u5e38\u6d45\u663e\u7684\uff0c\u4f46\u8111\u4e2d\u6709\u4e00\u5806\u4e71\u4e03\u516b\u7cdf\u7684\u8fd9\u4e9b\u201c\u7531\u5934\u201d\uff0c\u53cd\u5012\u4f7f\u6211\u65e5\u540e\u5bf9\u5f88\u591a\u5b66\u79d1\u90fd\u66f4\u5bb9\u6613\u5165\u95e8\u3002 \u6709\u5f88\u591a\u4eba\u5b66\u82f1\u8bed\u662f\u80cc\u5355\u8bcd\u7684\u3002\u6211\u5988\u4e00\u76f4\u4e0d\u76f8\u4fe1\u6211\u82f1\u8bed\u5f88\u597d\u7684\u7406\u7531\u5c31\u662f\u201c\u4ece\u6765\u6ca1\u770b\u6211\u80cc\u8fc7\u5355\u8bcd\u201d\u3002\u90a3\u662f\u56e0\u4e3a\uff0c\u5c0f\u5b66\u7684\u82f1\u8bed\u8001\u5e08\u4e0a\u8bfe\u6559\u8fc7\u201c\u5f00\u97f3\u8282\u201d\u3001\u201c\u95ed\u97f3\u8282\u201d\u4e4b\u7c7b\u7684\u77e5\u8bc6\uff0c\u4ee5\u53ca\u8bf8\u5982\u201coo\u201d\u3001\u201cee\u201d\u4e4b\u7c7b\u7684\u53d1\u97f3\u89c4\u5f8b\u3002\u6211\u77e5\u9053\u600e\u4e48\u8bfb\u5c31\u5927\u81f4\u77e5\u9053\u600e\u4e48\u62fc\u5199\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u800c\u4e14\u968f\u7740\u8bcd\u6c47\u91cf\u7684\u589e\u52a0\u800c\u589e\u52a0\u7684\u5e76\u4e0d\u662f\u8d1f\u62c5\uff0c\u53cd\u800c\u662f\u89c4\u5f8b\u6027\u3002\u5f53\u6211\u9047\u5230\u65b0\u8bcd\uff0c\u6211\u4e0d\u662f\u89c9\u5f97\u8d1f\u62c5\u5728\u52a0\u91cd\uff0c\u800c\u662f\u89c4\u5f8b\u6027\u7684\u53c8\u4e00\u6b21\u9a8c\u8bc1\u6216\u4f8b\u5916\u2014\u2014\u65e0\u8bba\u54ea\u4e2a\u60c5\u51b5\u90fd\u4ee4\u4eba\u5370\u8c61\u6df1\u523b\uff0c\u6839\u672c\u4e0d\u7528\u53e6\u5916\u518d\u82b1\u65f6\u95f4\u80cc\u3002 \u5f53\u7136\uff0c\u5bf9\u8003\u8bd5\u6210\u7ee9\u6beb\u4e0d\u4e0a\u5fc3\u624d\u662f\u6211\u4e0d\u80cc\u5355\u8bcd\u7684\u4e3b\u8981\u539f\u56e0\u3002\u6211\u4e0d\u89c9\u5f97\u77e5\u8bc6\u975e\u8981\u5728\u8d76\u5728\u8003\u8bd5\u4e4b\u524d\u5f04\u61c2\u3002\u4e8b\u5b9e\u4e0a\u51ed\u6211\u6765\u5f97\u53ca\u5f04\u61c2\u7684\u90e8\u5206\u5c31\u53ef\u4ee5\u8003\u53ca\u683c\u4e86\u3002\u6211\u5269\u4e0b\u7684\u65f6\u95f4\u5168\u90fd\u82b1\u5728\u5404\u79cd\u7a00\u5947\u53e4\u602a\u7684\u4e8b\u60c5\u4e0a\u3002 \u521d\u4e2d\u7684\u65f6\u5019\u5f88\u6d41\u884c\u300a\u72ee\u5b50\u738b\u300b\u3002\u6211\u4e5f\u5f88\u8ddf\u98ce\u5730\u4e70\u4e86\u4e00\u76d2\u72ee\u5b50\u738b\u7684\u5f55\u97f3\u5e26\u3002\u6211\u975e\u5e38\u559c\u6b22\u91cc\u9762\u7684Be Prepared\uff0c\u5230\u73b0\u5728\u90fd\u8fd8\u662f\u3002\u6211\u89c9\u5f97\u8fd9\u662f\u72ee\u5b50\u738b\u91cc\u9762\u6700\u597d\u542c\u7684\u6b4c\uff0c\u53ef\u662f\u4e00\u822c\u7684\u8d44\u6599\u90fd\u4e0d\u592a\u5f3a\u8c03\u8fd9\u9996\uff0c\u5927\u5bb6\u4f3c\u4e4e\u89c9\u5f97Can you feel the love tonight\u624d\u662f\u4e3b\u6253\u6b4c\u3002\u4e5f\u8bb8\u540e\u8005\u653f\u6cbb\u6bd4\u8f83\u6b63\u786e\u5427\u3002 \u521d\u4e2d\u7684\u65f6\u5019\u8fd8\u6d41\u884c\u5f88\u591a\u82f1\u8bed\u6d41\u884c\u6b4c\uff0c\u6240\u4ee5\u514d\u4e0d\u4e86\u63a5\u89e6\u5230\u5f88\u591a\u82f1\u8bed\u5355\u8bcd\u3002\u4e3a\u4e86\u5531\u5f97\u50cf\u539f\u5531\uff0c\u6211\u5fc5\u987b\u786e\u5207\u5730\u77e5\u9053\u8fd9\u4e9b\u751f\u8bcd\u662f\u600e\u4e48\u8bfb\u7684\uff0c\u6240\u4ee5\u4f1a\u67e5\u5b57\u5178\u3002Be prepared\u7684\u6b4c\u8bcd\u91cc\u9762\u6709\u4e00\u4e2a\u6781\u5176\u53d8\u6001\u7684\u8bcd\u53ebquid pro quo\u3002\u6574\u53e5\u662f\u8fd9\u6837\u7684\uff1aOf course, quid pro quo, you are expected to take certain duty on board\u3002 \u6574\u53e5\u6211\u90fd\u80fd\u8bfb\u61c2\u4e86\uff0c\u4e2d\u95f4quid pro quo\u5c31\u8ba9\u6211\u5f88\u90c1\u95f7\u3002\u7b2c\u4e00\u76f4\u89c9\u662f\u8fd9\u662f\u4e00\u4e2a\u4eba\u7684\u540d\u5b57\u3002\u76f8\u5f53\u4e8e\u201cOf course, Mr. Black, you are expected ...\u201d\u8fd9\u79cd\u60c5\u51b5\u3002\u4f46\u6b7b\u677f\u7684\u521d\u4e2d\u8bfe\u5802\u82f1\u8bed\u544a\u8bc9\u6211\uff0c\u4eba\u540d\u662f\u8981\u5927\u5199\u7684\uff0c\u800c\u8fd9\u4e09\u4e2a\u9e1f\u8bcd\u5374\u662f\u5c0f\u5199\u3002\u4e8e\u662f\u6211\u5c31\u67e5\u5b57\u5178\uff0c\u77e5\u9053\u8fd9\u539f\u6765\u4e0d\u662f\u82f1\u8bed\u3002\u610f\u601d\u603b\u7b97\u641e\u61c2\u4e86\uff0c\u4f46\u660e\u660e\u662f\u82f1\u6587\u6b4c\u8bcd\u91cc\u9762\u63d2\u4e2a\u4e0d\u662f\u82f1\u8bed\u7684\u4e1c\u897f\uff0c\u8ba9\u6211\u975e\u5e38\u90c1\u95f7\u3002\u6240\u4ee5\u6211\u4ece\u6b64\u5bf9\u82f1\u8bed\u91cc\u5939\u70b9\u602a\u8bcd\u7684\u73b0\u8c61\u5f88\u7559\u610f\u3002 \u662f\u7684\u6211\u89c9\u5f97\u6211\u521d\u4e2d\u5c31\u77e5\u9053quid pro quo\u7684\u610f\u601d\u771f\u662f\u975e\u5e38\u4e86\u4e0d\u5f97\uff01\u6211\u8981\u8dd1\u5230\u83dc\u5e02\u573a\u53bb\u6293\u4f4f\u6bcf\u4e00\u4e2a\u963f\u59e8\u8bf4\u201c\u5582\u5582\u4f60\u77e5\u4e0d\u77e5\u9053\u6211\u521d\u4e2d\u5c31\u61c2quid pro quo\u7684\u610f\u601d\u5566\uff01\u201d\u7136\u540e\uff0c\u6bcf\u5f53\u6211\u8eab\u65c1\u8c01\u9047\u5230\u4e86quid pro quo\u4e4b\u540e\u8138\u9732\u96be\u8272\u7136\u540e\u53bb\u67e5\u5b57\u5178\u7684\u65f6\u5019\uff0c\u6211\u773c\u4e2d\u5fc5\u7136\u4f1a\u95ea\u8fc7\u4e00\u4e1d\u51b7\u7b11\u3002 Calligraphy\u8fd9\u4ef6\u4e8b\u6211\u4e5f\u662f\u633a\u65e9\u77e5\u9053\u7684\u3002Mr. Bean\u91cc\u9762\u6709\u4e00\u96c6\u662f\u4ec0\u4e48\u5b66\u6821\u7684\u5f00\u653e\u65e5\u3002\u5176\u4e2d\u6709\u4e00\u4e2a\u5c55\u793a\u662f\u4e00\u4e2a\u8001\u4eba\uff08John Clegg\u9970\uff09\u7a7f\u7740\u50e7\u4fa3\u7684\u670d\u88c5\u8868\u6f14calligraphy\u3002Mr. Bean\u53c8\u6ca1\u5b89\u597d\u5fc3\u3002 Calligraphy\u662f\u4e00\u4e2a\u5f88\u8ff7\u4eba\u7684\u827a\u672f\u3002\u4e2d\u4e16\u7eaa\u521d\u671f\u5317\u6b27\u50e7\u4fa3\u6284\u5723\u7ecf\u5c31\u8981\u8ffd\u6c42calligraphy\u3002\u5199\u8fd9\u73a9\u610f\u513f\u662f\u4e00\u4e2a\u7ec6\u81f4\u6d3b\u3002\u8981\u7528\u5230pen\u3002\u4e4b\u6240\u4ee5\u8fde\u201c\u94a2\u7b14\u201d\u90fd\u8981\u7528\u82f1\u8bed\u5355\u8bcd\u4e0d\u662f\u6211\u60f3\u88c5ABC\uff0c\u800c\u662f\u8fd9\u91cc\u7684pen\u786e\u5b9e\u4e0d\u662f\u5728\u6307\u201c\u94a2\u7b14\u201dOK\uff1f\u5723\u7ecf\u8fd9\u4e48\u591a\u5b57\uff0c\u5199\u4e00\u4e2a\u5b57\u8fd9\u4e48\u6162\uff0c\u8fd9\u4e9b\u50e7\u4fa3\u5929\u5929\u5c31\u5e72\u8fd9\u4e2a\u5c31\u53ef\u4ee5\u5e72\u4e00\u8f88\u5b50\u3002 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expected...","src":"https:\/\/i0.wp.com\/images.wikia.com\/disneyvillains\/images\/7\/78\/Be_Prepared_2.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":9243,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9243","url_meta":{"origin":9288,"position":4},"title":"\u4e2d\u56fd\u548c\u82f1\u56fd\u7edf\u8ba1\u529b\u5b66\u5bb6\u5728\u9ad8\u5206\u5b50\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u8d21\u732e","author":"Andrew","date":"2025\u5e748\u67082\u65e5","format":false,"excerpt":"\u6211\u4eec\u90fd\u77e5\u9053Flory--Huggins\u6eb6\u6db2\u7406\u8bba\u4e2d\u7684\u6df7\u5408\u71b5\uff0c\u5c31\u662f\u628a\u7406\u60f3\u6eb6\u6db2\u7684\u6df7\u5408\u71b5\u8868\u8fbe\u5f0f\u4e2d\u7684\u6469\u5c14\u5206\u6570\u6539\u6210\u4e86\u4f53\u79ef\u5206\u6570\u3002\u4ee5\u4e8c\u5143\u6db2\u6001\u6df7\u5408\u7269\u4e3a\u4f8b\uff0c$$\\Delta_\\text{mix}G^\\text{id}=-T\\Delta_\\text{mix}S^\\text{id}=RT\\left[n_1\\ln x_1+n_2\\ln x_2\\right]$$\u800cFlory--Huggins\u7406\u8bba\u7ed9\u51fa\u7684\u5c0f\u5206\u5b50\u6eb6\u5242+\u7ebf\u5f62\u9ad8\u805a\u7269\u6eb6\u8d28\u7684\u7ed3\u679c\u662f\uff1a$$\\Delta_\\text{mix}S=-R\\left[n_1\\ln\\varphi_1+n_2\\ln\\varphi_2\\right]$$\u4ee5\u4e0a\u8ba8\u8bba\u90fd\u5047\u5b9a$\\Delta_\\text{mix}H=0$\uff0c\u6216\u8005\u9650\u4e8e\u683c\u5b50\u6a21\u578b\u6765\u8bf4\u5c31\u662f\u4e0d\u540c\u6784\u5f62\u7684\u5185\u80fd\u76f8\u540c\u3002\u8fd9\u88ab\u79f0\u4e3a\u65e0\u70ed\uff08athermal\uff09\u6eb6\u6db2\uff08\u662f\u56e0\u4e3a\u7113\u5386\u53f2\u4e0a\u88ab\u79f0\u4e3a\u201cheat\u201d\uff0c\u5176\u5b9e\u8fd9\u8ddf\u70ed\u5bb9\u6216\u71b5\u4e0d\u76f4\u63a5\u76f8\u5173\uff0c\u53cd\u800c\u662f\u76f8\u4e92\u4f5c\u7528\u52bf\u80fd\u7684\u4f53\u73b0\uff09\u3002\u5982\u679c\u6309\u7167\u60ef\u4f8b\u7528\u76f8\u540c\u6761\u4ef6\u4e0b\u7684\u7406\u60f3\u6df7\u5408\u7269\u4f5c\u4e3a\u6807\u51c6\u6001\uff0c\u90a3\u4e48Flory--Huggins\u7684\u7ed3\u679c\u4f53\u73b0\u7684\u7ed3\u8bba\u5c31\u662f\uff0c\u4ec5\u56e0\u5206\u5b50\u4f53\u79ef\u4e0d\u540c\uff0c\u4e5f\u4f1a\u5236\u9020\u51fa\u975e\u96f6\u7684\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\uff0c\u4e14\u8fd9\u4e2a\u8d85\u989d\u6df7\u5408\u81ea\u7531\u80fd\u662f\u7eaf\u71b5\u53d8\u3002 \u65e9\u671f\u8ba4\u4e3a\uff0c\u5206\u5b50\u4f53\u79ef\u4e0d\u540c\uff0c\u662f\u8981\u901a\u8fc7\u5b83\u4eec\u9020\u6210\u4e86\u76f8\u4e92\u4f5c\u7528\u52bf\u7684\u4e0d\u5bf9\u79f0\uff0c\u5373\u975e\u96f6\u7684\u4ea4\u6362\u80fd$w\\equiv w_{AB}-\\left(1\\middle\/2\\right)\\left(w_{AA}+w_{BB}\\right)$\uff0c\u6bd5\u7adf\u5206\u5b50\u5927\u5c0f\u9996\u5148\u5c31\u5f71\u54cd\u8272\u6563\u529b\u3002\u5230\u4e86\u5927\u69821930\u5e74\u4e2d\u53f6\uff08\u57281936\u5e74\u7684\u6cd5\u62c9\u7b2c\u5b66\u4f1a\u7b2c65\u6b21\u4e00\u822c\u8ba8\u8bba\u4e2d\uff09\uff0c\u5927\u5bb6\u624d\u63a5\u53d7\u4e0d\u540c\u5206\u5b50\u5c3a\u5bf8\u7684\u65e0\u70ed\u6df7\u5408\u7269\u6709\u8d85\u989d\u71b5\u3002R. Fowler\u63d0\u51fa\u5927\u4e00\u70b9\u7684\u5206\u5b50\u53ef\u4ee5\u8003\u8651\u5360\u4e24\u4e2a\u683c\u5b50\u3002\u4ed6\u548cG. Rushbrook\u53d1\u8868\u7684\u8fd9\u79cd\u8ba1\u7b97\u7ed3\u679c\u8bc1\u5b9e\u4e86\u8fd9\u4ef6\u4e8b\u3002\u4ec5\u4ec5\u4f5c\u51fa\u8fd9\u4e00\u5c0f\u6b65\u7684\u63a8\u5e7f\uff0c\u6570\u5b66\u63a8\u5bfc\u7684\u96be\u5ea6\u5c31\u5927\u589e\u3002\u539f\u6587\u53ea\u8ba8\u8bba\u4e86$N_1\\ll N_2$\u6216$N_1\\gg N_2$\u7684\u60c5\u51b5\u3002H. Bethe\u63d0\u51fa\u4e86\u4e00\u79cd\u65b9\u6cd5\uff0c\u73b0\u5728\u79f0\u4e3aBethe--Peierls\u8fd1\u4f3c\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u8003\u8651\u4e8c\u4f53\u76f8\u5173\u6027\u4e0b\u7684\u6784\u5f62\u6570\uff0c\u5373\u53ef\u5f97\u5230\u6982\u7387$p_{ij},\\quad i,j=A,B$\u3002\u8fd9\u4e2a\u65b9\u6cd5\u8fc5\u901f\u88ab\u5f20\u5b97\u71e7\u548cA. Miller\u7b49\u7528\u4e8e\u8003\u8651\u5927\u5206\u5b50\u6eb6\u8d28\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4ece\u4e8c\u805a\u4f53\u3001\u4e09\u805a\u4f53\u4e00\u76f4\u63a8\u5e7f\u5230\u4e00\u822c\u7684$r$\u805a\u4f53\u3002\u8fd9\u4e24\u4e2a\u4eba\u9760Bethe\u65b9\u6cd5\u5199\u4e0b\u6784\u5f62\u6570\uff0c\u5f97\u5230\u65e0\u70ed\u6eb6\u6db2\u7684\u6df7\u5408\u71b5\u53d8\u90e8\u5206\u3002W. Orr\u8fdb\u4e00\u6b65\u628aBethe\u8fd1\u4f3c\u4e0b\u7684\u6df7\u5408\u7113\u4e5f\u5199\u51fa\u6765\u4e86\u3002E. Guggenheim\u7528\u53e6\u4e00\u79cd\u66f4\u4f18\u96c5\u7684\u65b9\u6cd5\uff0c\u5f97\u51fa\u4e86\u8ddf\u7528Bethe\u65b9\u6cd5\u4e00\u6837\u7684\u7ed3\u679c\uff0c\u5e76\u8bc1\u660e\u4e24\u79cd\u65b9\u6cd5\u662f\u7b49\u4ef7\u7684\u3002\u8fd9\u4e9b\u6765\u81ea\u82f1\u56fd\uff08\u548c\u6211\u56fd\u5f20\u5b97\u71e7\u5728\u82f1\u56fd\u7559\u5b66\u65f6\uff09\u7684\u8d21\u732e\uff0c\u57fa\u672c\u7cfb\u7edf\u6027\u5730\u7ec8\u7ed3\u4e86\u805a\u5408\u7269\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u683c\u5b50\u7406\u8bba\u5de5\u4f5c\u3002\u53ef\u4ee5\u53c2\u8003A. Miller\u548cE. Guggenheim\u7684\u4e24\u672c\u4e66\uff1a A. Miller (1948), The Theory of Solutions of High Polymers, Clarendon E. Guggenheim (1952), Mixtures, Clarendon\u4e5f\u53ef\u4ee5\u53c2\u8003H. Tompa\u7684\u4e66\uff1a H. Tompa (1956), Polymer Solutions, Butterworths \u8fd9\u4e2aH. Tompa\u4e5f\u662f\u503c\u5f97\u4e00\u8bf4\u7684\uff0c\u4f46\u6211\u53ef\u80fd\u8981\u5c06\u5728\u53e6\u4e00\u7bc7\u6587\u7ae0\u91cc\u8bb2\u3002 \u6211\u4eec\u4eca\u5929\u6240\u719f\u77e5\u7684Flory--Huggins\u5c5e\u4e8e\u540c\u65f6\u671f\u7f8e\u56fd\u4eba\u7684\u5de5\u4f5c\u3002\u6211\u4e4b\u524d\u7684\u6587\u7ae0\u63d0\u5230\uff0c\u662fM. Huggins\u7a0d\u5fae\u6bd4P. Flory\u65e9\u51e0\u4e2a\u6708\u5f00\u59cb\u63a8\u5bfc\u9ad8\u5206\u5b50\u6eb6\u6db2\u7684\u683c\u5b50\u6a21\u578b\uff0c\u4f3c\u4e4e\u8fd9\u79cd\u540c\u65f6\u6027\u662f\u5de7\u5408\uff0c\u4f46\u5176\u5b9eFlory\u8fd9\u4e2a\u505a\u6cd5\u662f\u53d7\u5fb7\u56fd\u5316\u5b66\u5bb6K. Meyer\u7684\u5efa\u8bae\u505a\u7684\u3002K. Meyer\u548cH. Mark\u5408\u8457\u4e86\u4e16\u754c\u4e0a\u7b2c\u4e00\u672c\u9ad8\u5206\u5b50\u79d1\u5b66\u7684\u6559\u79d1\u4e66\u3002 \u503c\u5f97\u5f3a\u8c03\u7684\u662f\uff0c\u4eca\u5929\u7684Flory--Huggins\u5f62\u5f0f\uff0c\u662fGuggenheim\u4e00\u822c\u5f62\u5f0f\u4e2d\u914d\u4f4d\u6570$z\\to\\infty$\u7684\u7279\u6b8a\u7ed3\u679c\uff0c\u6240\u4ee5\u8868\u8fbe\u5f0f\u4e2d\u4e0d\u663e\u542b$z$\uff08\u4ea4\u6362\u71b5\u53d8\u90e8\u5206\u4e0d\u542b$z$\uff0c\u7113\u53d8\u5bf9$z$\u7684\u4f9d\u8d56\u6027\u5305\u5728\u201c\u76f8\u4e92\u4f5c\u7528\u53c2\u6570\u201d $\\chi$ \u7684\u5b9a\u4e49\u4e2d\u4e86\uff09\u3002\u54ea\u6015\u662f\u9650\u4e8e\u5bfc\u51faFlory--Huggins\u7684\u4ea4\u6362\u71b5\u5f62\u5f0f\uff0c\u4e5f\u6709\u4e0d\u540c\u7684\u6570\u683c\u5b50\u65b9\u6cd5\u3002\u4eca\u5929\u8bb8\u591a\u4e2d\u6587\u9ad8\u5206\u5b50\u7269\u7406\u6559\u79d1\u4e66\u4e0a\u7684\u6570\u6cd5\uff0c\u5c31\u8ddfFlory\u5728\u81ea\u5df1\u7684\u4e66\u4e2d\u7684\u6570\u6cd5\u6709\u70b9\u4e0d\u540c\uff0c\u4f46\u90fd\u7528\u4e0d\u540c\u7684\u8fd1\u4f3c\u4e3b\u5f20\u51d1\u51fa\u4e86\u76f8\u540c\u7684\u6700\u540e\u7ed3\u679c\u3002\u5176\u4e2d\u4e00\u79cd\u5199\u6cd5\u9700\u8981\u8bf4\u201c\u5047\u5b9a\u2026","rel":"","context":"In 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